document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488247>Question 488247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If we choose x from the set of values bigger than 0, is y = x²  a function of x? explain<BR>\n" );
document.write( " <BR>\n" );
document.write( "If we choose y from the set of values bigger than 0, is y = x² a function of y? explain<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333328 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = x^2 makes y a function of x.<BR>\n" );
document.write( "the independent variable is x and the dependent variable is y.<BR>\n" );
document.write( "x^2 = y makes x^2 a function of y.<BR>\n" );
document.write( "the independent variable is y and the dependent variable is x^2.<BR>\n" );
document.write( "if we let z = x^2, then:<BR>\n" );
document.write( "x^2 = y becomes z = y<BR>\n" );
document.write( "z is considered a function of y because it depends on the value of y.<BR>\n" );
document.write( "you would solve this like you would solve any equation.<BR>\n" );
document.write( "if y = 5, then z = 5<BR>\n" );
document.write( "since z = x^2, this means that x^2 = 5.<BR>\n" );
document.write( "suppose you had:<BR>\n" );
document.write( "x^2 = y-3<BR>\n" );
document.write( "x^2 is still a function of y because it depends on the value of y.<BR>\n" );
document.write( "if y = 5, x^2 = y - 3 = 5 - 3 = 2<BR>\n" );
document.write( "you get x^2 = 2 when y = 5<BR>\n" );
document.write( "i believe this to be true, but i won't swear to it.<BR>\n" );
document.write( "there may be some rule that says you can't do this, but i haven't seen it.<BR>\n" );
document.write( "in practice, you can set anything equal to anything else.<BR>\n" );
document.write( "the dependent variable is a function of the independent variable.<BR>\n" );
document.write( "the equation determines the value of the dependent variable based on the value of the independent variable.<BR>\n" );
document.write( "x^2 is a function of y meets that definition.<BR>\n" );
document.write( "the value of x^2 is dependent on the value of y.<BR>\n" );
document.write( "the right side of that equation doesn't have to be just y.<BR>\n" );
document.write( "it can be any expression involving y.<BR>\n" );
document.write( "x^2 = y^3 + 5y - 3 would be an example.<BR>\n" );
document.write( "x^2 is a function of y.<BR>\n" );
document.write( "when y = 3, x^3 = 27 + 15 - 3 which becomes:<BR>\n" );
document.write( "x^2 = 39\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );